For one-to-one I was thinking of the Unicode Character Database single-character upper, lower, and title case entries in the UnicodeData.txt file [1] -- i.e. the simple case mappings [2].

The one-to-many mappings are specified in SpecialCasing.txt. Some are locale independent (like my German sharp/double S example) and others are locale aware (like the Turkish example). For the locale aware mappings you need to ensure you are setting the language/locale correctly in your language of choice, or that the language is doing the right thing.

[1] https://www.unicode.org/Public/UCD/latest/ucd/UnicodeData.tx...

[2] https://www.unicode.org/reports/tr44/#Casemapping

[3] https://www.unicode.org/Public/UCD/latest/ucd/SpecialCasing....